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Assignment Demand and Supply Function

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Added on  2020-04-21

Assignment Demand and Supply Function

   Added on 2020-04-21

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MathsStudent Name:Student Number:Lecturer Name:5th November 2017
Assignment Demand and Supply Function_1
Section A:1.The demand function in a competitive market is qD=22–0.2p, while the supply is givenby qs=0.4p–8. a)What is the inverse supply function?Solution0.4p=qs+8p=qs0.4+80.4p=2.5qs+20b)Draw a sketch graph of these two functions and identify where they intersect p and qaxes.c)Find the equilibrium price and quantity in this market. SolutionThe equilibrium price is $50 and the equilibrium quantity is 12.
Assignment Demand and Supply Function_2
d)Calculate the price elasticity of supply when quantity is 15. Interpret your result. SolutionFor supply we have: p=2.5Q+20For demand we have: p=−5Q+110From above ∆Q∆P = 2.5; the gradient of p=2.5Q+20The associated price when quantity is 15 is;P=2.5*15+20=57.5Point Price Elasticity of Quantity = (% change in Quantity)/(% change in Price)PointPriceElasticityofQuantity=(∆QQ)/(∆PP)Point Price Elasticity of Quantity = (PQ)(∆Q∆P)Elasticity = 2.5 *(57.5/15) = 9.58As can be seen, the elasticity is greater than 1; this means that a given percentagechange in price leads to a larger change in quantity supplied.e)Calculate the consumer surplus at the equilibrium point.Solution
Assignment Demand and Supply Function_3
The area under the curve is shown by the arrow represents the consumer surplus;Area=12∗10∗50=250Thus the consumer surplus at the equilibrium point is 250.2.An inverse demand function for a monopoly is given by P=224–6Q. The monopoly’saverage cost function is C36+4Q32Q2 . a)Write down an expression for total revenue, TR, then find the marginal revenuefunction. SolutionTR=P∗QTR=(224−6Q)Q¿224Q−6Q2Marginal revenue function:MR=dTRdQ=224−12QConsumer Surplus
Assignment Demand and Supply Function_4

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